An Fe-based amorphous alloy ribbon receives attention as a magnetic core material of a transformer, a motor, a choke coil, a sensor and the like, because of excellent soft magnetic properties, particularly a low core loss among them. It has been practically used for various magnetic cores, parts and apparatuses. Among the Fe-based amorphous alloy ribbons, an FeSiB-based amorphous alloy ribbon has been widely used in particular, because it shows comparatively a high saturated magnetic flux density Bs and superior thermal stability. However, the FeSiB-based amorphous alloy ribbon has problems that the magnetic core becomes large because the FeSiB-based amorphous alloy ribbon has lower Bs than a silicon steel sheet, and that the magnetic core generates a high level of noise. As a method for increasing Bs in the Fe-based amorphous alloy ribbon, there have been practically carried out methods of: increasing an amount of Fe which bears magnetism; inhibiting thermal stability from deteriorating due to increased amount of Fe by adding Sn, S or the like; adding C; or adding C and P. JP-A-05-140703 discloses a method of increasing Bs by employing a composition of FeSiBCSn, enhancing the formability of amorphous in an Fe-rich area by adding Sn. On the other hand, JP-A-2002-285304 discloses a method of increasing Bs by employing a composition of FeSiBCP, greatly increasing the Fe content specifically by adding P into a limited composition range of Fe, Si, B and C. Regarding reducing magnetostriction, which is necessary for reducing a noise level, the saturation magnetostriction of the Fe-based amorphous alloy ribbon is approximately proportional to the square of Bs. Accordingly, the Fe-based amorphous alloy ribbon having high Bs and low magnetostriction has not been realized yet. For this reason, an amorphous or a nano-crystalline alloy ribbon with low Bs and low magnetostriction has been used for the magnetic core and an applied product with the use of the magnetic core, which is required not to cause a problem of noise.    [Patent Document 1]    JP-A-05-140703 ((0008) to (0010), and FIG. 1)    [Patent Document 2]    JP-A-2002-285304 ((0010) to (0016), and Table 1)